Operads of compatible structures and weighted partitions
arXiv:0706.2196 · doi:10.1016/j.jpaa.2008.04.009
Abstract
In this paper we describe operads encoding two different kinds of compatibility of algebraic structures. We show that there exist decompositions of these in terms of black and white products and we prove that they are Koszul for a large class of algebraic structures by using the poset method of B. Vallette. In particular we show that this is true for the operads of compatible Lie, associative and pre-Lie algebras.
16 pages, main result about Koszulness generalized to a large class of compatible structures
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Cited by in corpus (16)
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- Freeness theorems for operads via Gröbner bases
- Cohomology and deformations of compatible Hom-Lie algebras
- Matching Rota-Baxter algebras, matching dendriform algebras and matching pre-Lie algebras
- A classification of nilpotent compatible Lie algebras
- Operad profiles of Nijenhuis structures
- Lie and Jordan products in interchange algebras
- Universal enveloping algebra of a pair of compatible Lie brackets
- On the computation of Manin products for operads
- Homotopy Transfer Theorem for Linearly Compatible Di-algebras
- Compatible -algebras